Today
Introduction
Probabilistic Reasoning
Sequential Decision Making Game Theory
(A peek at) Machine Learning Argumentation
AI & Ethics
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Recap
percepts
Environment
sensors
AI Systems operate in environments
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actions
effectors
Recap
Environments are:
‚ Acessibleornot.
‚ Deterministic/stochastic/non-deterministic ‚ StaticorDynamic
‚ SequentialorEpisodic
‚ Discreteorcontinuous
‚ Observable/Fullyobservable/partiallyobservable.
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Partial observability
Full observability: Chess, Go, Ur
Partial observability: Poker, Starcraft, Fornite, 0AD . . .
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Real world: Partially observable environment
(mystorybook.com/books/42485)
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Real world: Partially observable environment
( & /Google )
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Partial observability
Partial observability can arise for many reasons. ‚ Worldstructurevs.sensorability.
‚ Sensornoise.
‚ Computationalcomplexity.
Partial observability Ñ uncertainty. This will allow us to derive abstract models.
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Uncertainty
Say you’re at the Strand campus and you have to catch a flight at Heathrow Airport When do you leave?
Let action At: you leave for airport t minutes before the flight
Example: A60: you leave one hour before
get me there on time? Problems:
1. partialobservability(tubestate,othertravelers’plans,etc.)
2. noisysensors(GoogleMaps’trafficupdates)
3. uncertaintyinactionoutcomes(strike,toomanyleaves,issueswiththesignalling,etc.) 4. immensecomplexityofmodellingandpredictingtraffic
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Example: Modelling Uncertainty
Making statements based on partial observations is tricky 1. risks falsehood: “A90 will get me there on time”
2. leadstoconclusionsthataretooweakfordecisionmaking:
“A90 will get me there on time if there are fewer than 300 people at the the first two stops, and there is no strike and the signalling remains intact etc.”
(bbc.co.uk) ( )
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Uncertainty
Play safe: A1440 might reasonably be said to get me there on time but you’d have to stay overnight in the airport . . .
Can we do something better?
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Methods for handling uncertainty
Use probability
‚ Giventheavailableevidence,
A25 will get me there on time with probability 0.04 Probabilistic assertions summarize effects of
‚ laziness: failure to enumerate exceptions, qualifications, etc. ‚ ignorance: lack of relevant facts, initial conditions, etc.
Even with probabilistic assumptions there are still issues: Computational complexity, obtaining values, semantics.
‚ Wewillconsiderthecomputationalissuesinsomedetail.
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Aside
Fuzzy logic handles degree of truth NOT uncertainty ‚ Givena142cm-tallponywehave
‚ ShortPonyistruetodegree0
‚ MediumPonyistruetodegree0.5 ‚ TallPonyistruetodegree0.5
Truth value 1
Medium
Truth value 0
127 cm
137cm
147cm
Short
Tall
(4’2’’)
(4’4’’)
(4’6’’)
Pony Height
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Probability
Subjective or Bayesian probability:
‚ Probabilitiesrelatepropositionstoone’sownstateofknowledge
‚ PpA25q“0.04.Knowingthatnotrafficissueswasreported(sayinthemorning),
makes it more likely
PpA25|no reported traffic issuesq “ 0.06 Probabilities of propositions change with new evidence:
PpA25|no reported traffic issues, leaving at 5 a.m.q “ 0.15 PpA25|no reported traffic issues, leaving at 9 a.m.q “ 0.03
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Making decisions under uncertainty
Suppose I believe the following:
PpA25 gets me there on time|…q
PpA90 gets me there on time|…q P pA120 gets me there on time| . . .q P pA1440 gets me there on time| . . .q
Which action to choose?
“ 0.04 “ 0.70 “ 0.95 “ 0.9999
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Methods for handling uncertainty
Depends on our preferences for missing flight vs. airport cuisine, sleeping on a bench, and so on.
Utility theory is used to represent and infer preferences Decision theory = utility theory + probability theory We will come back to decision theory in a few weeks.
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Summary
There is a lot of uncertainty
Uncertainty can be modelled very well by using probabilities
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